Illicit radioactive sources can potentially appear in a wide range of public venues. One element in a plan for managing such sources involves searching for them in venues at risk and tracking them in real time when they are detected. A treatment of source tracking using multiple directional detectors in a probabilistic framework is given. The performance of a prototype directional detector based on these methods was characterized in the laboratory. Instances where the performance of a directional detector is not immune to the effects of shielding are identified.